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Offline Centres

Q.

In a regular hexgon, each corner is at a distance 'r' from the centre. Identical charges of magnitude 'Q' are placed at 5 corners. The field at the centre is $(K = \frac{1}{4 {πϵ}_{0}})$

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a

$\frac{6 kQ}{r^{2}}$

b

$k Q / r^{2}$

c

Zero

d

$\frac{5 kQ}{r^{2}}$

answer is A.

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Detailed Solution

$\begin{array}{l} {\vec{E}}_{c} = \vec{E_{1}} + \vec{E_{2}} + \vec{E_{3}} + \vec{E_{4}} + \vec{E_{5}} \\ {\vec{E}}_{c} = (\vec{E_{1}} + \vec{E_{4}}) + (\vec{E_{2}} + \vec{E_{5}}) + \vec{E_{3}} = 0 + 0 + \vec{E_{3}} \\ E_{C} = E_{3} = \frac{1}{4 {πE}_{0}} \frac{Q}{r^{2}} \end{array}$

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